According to a known method for forming a gear, a die on which a predetermined tooth profile is formed is pressed to a cylindrical blank to form a gear with a predetermined configuration. In those circumstances, for example, a round die for form rolling having a tooth profile which is engageable with a gear to be manufactured is applied. Generally, two round dies for form rolling are rotated and are moved to be close to a work piece to press the dies to the work piece. The round dies for form rolling are gradually pressed to move to a final position for forming a gear.
In a case where a gear is formed by using a round die for form rolling, first, an addendum portion of a tooth of the round die for form rolling comes in contact with a surface of a work piece. Intermittently pressed indentations are formed on the surface of the work piece by the contact of the addendum portion of the tooth of the round die. By gradually pressing the round die for form rolling to the work piece, a tooth (teeth) of the round die for form rolling thrusts into the work piece to form a bottom land portion of the gear. On the other hand, at a portion adjacent to the bottomland portion, a blank of the work piece is bulged to form a tooth portion of the gear. A desired configuration of the gear is formed when the round die for form rolling is pressed to a predetermined position relative to the work piece.
FIG. 2 shows a state where a die 20 starts contacting a work piece 10 (i.e., contacting state of the die 20) in a manufacturing process for a known involute gear. The die 20 is rotated by an actuation of a driving mechanism. The work piece 10 is driven by the die 20. Generally, another die 20 is arranged at an opposite side of the work piece 10, and the work piece 10 is pressed by a pair of the dies 20. In a state shown in FIG. 2, an addendum portion 21 of the die 20 presses into the work piece 10 to form an indentation 11. By moving an axis X2 of the die 20 to an axis X1 of the work piece 10 while rotating the die 20, the addendum portions 21 of the die 20 are gradually and consecutively pressed into the indentation 11 so that a dimension of the indentation 11 are enlarged broader and deeper. A base material of the work piece 10 positioned at the indentation 11 is bulged at both sides of the indentation 11 to form gear teeth.
FIG. 3 shows a mid-way state during a form rolling where the addendum portion 21 of the die 20 thrusts into, or presses into the work piece 10 to some extent. The die 20 moves to be closer to the work piece 10 while rotating, presses into the work piece 10 to form the indentation 11, and the addendum portion 21 of the die 20 simultaneously presses the work piece 10 in a radial direction to form the indentation 11 to be deeper and in a circumferential direction to expand the indentation 11 to be broader when the die 20 moves to be away from the work piece 10 so that adjacent portions of the indentation 11 are plastically deformed to form gear teeth.
FIG. 4 shows a state where the pressing of the die 20 into the work piece 10 is completed. Each tooth 12 of a gear W formed by the form rolling is engaged with teeth 22 of the die 20 without a backlash. In those circumstances, a tooth depth of the gear W corresponds to a tooth depth of the die 20. The gear W includes a base circle C1 having a radius rg1 whereas the die 20 includes a base circle C2 having a radius rg2. Each of the teeth 12 includes an involute tooth profile, and a pitch circle Cp2 of the die 20 is tangent to a pitch circle Cp1 of the gear W at a pitch point p. The pitch circle Cp1 has a radius rp1, and the pitch circle Cp2 has a radius rp2. The pitch point p corresponds to a point of intersection of a line connecting a center X1 of the gear W, a center X2 of the die 20, a common tangent L of the base circle C1 of the gear W, and the base circle C2 of the die 20. An angle formed by the line connecting the center X1 of the gear W and the center X2 of the die 20 and a perpendicular line drawn from the center X1 of the gear W, or the center X2 of the die 20, to the common tangent L, corresponds to a working pressure angle αw. The working pressure angle αw is defined when meshing two involute gears, and thus, the working pressure angle is varied when a distance between centers of the gears is varied.
On the other hand, each gear includes a pressure angle, which is defined when a pitch point overlaps a reference circle of the gear. The reference circle is defined for each gear or each die as a reference for determining parameters for designing gears or dies including the number of teeth, a module, a pressure angle, a helix angle, an addendum modification coefficient, or the like. Hereinafter, “pressure angle” indicates the pressure angle defined on the reference circle.
FIG. 5 is an explanatory view showing changes in configuration of the work piece 10. A surface of the work piece 10 before a form rolling process is indicated as d0 in FIG. 5. A portion indicated as a region A2 is pressed by the form rolling, and a base material moved from the pressed region A2 is assumed to have a volume of region A1 to form an addendum portion. Further, FIG. 5 illustrates addendum circle d1 and dedendum circle d2.
Conventionally, a gear configuration of the die 20 is designed on the basis of a configuration of the gear W to be manufactured. For example, specifications for forming the die 20 includes the number of teeth, a module, a pressure angle, a helix angle, an addendum modification coefficient, or the like. In those circumstances, generally, a module, a pressure angle, and a helix angle of the gear W are most likely applied as they are for determining the configuration of the die 20, and an addendum modification coefficient is fine-tuned as necessity arises. Thus, man-hours and labor for designing the die 20 are reduced, and the die 20 for forming the gear W with a desired configuration is readily attained. Generally, a diameter of the die 20 differs from a diameter of the gear W and the number of the gear tooth of the die 20 is assumed to be greater than the number of the gear tooth of the gear W.
In order to make the involute gears engage each other appropriately, base pitches of the respective involute gears have to accord to each other. The base pitch corresponds to a pitch measured along a common perpendicular between tooth profiles of a particular tooth and another tooth adjacent to the particular tooth. Namely, even if configurations of teeth and the number of teeth of the both gears differ from each other, the gears engage with each other appropriately as long as the feed distances between the teeth are the same. The base pitch P is generally defined as follows using a module m and a pressure angle α of the gear.P=π·m·cos α  [1]
Thus, conventionally, the module m and the pressure angle α of the die 20 can differ from those of the gear W. However, settings of degrees of the module m and the pressure angle α of the die 20 relative to the module and the pressure angle of the gear W, are not utilized in known methods and constructions.
According to the known form rolling method, a configuration of a die is designed assuming a meshed state of the die and a gear when the form rolling is completed. Accordingly, for example, when forming a bottom land portion of the gear by pressing the die into a work piece, there is a drawback that a contacting position of a tooth of the die to the work piece fluctuates in a circumferential direction of the work piece with each contact of the tooth. In other words, in a state where the gear is completely formed, the gear and the die are tangent to each other at a respective pitch circle to be appropriately engaged. Generally, a pitch on a reference circle of the die and a pitch on the pitch circle are considered for designing dies, however, an addendum pitch (i.e., pitch between addendum portions of adjacent teeth) is not particularly considered when designing the dies. Thus, positions of indentations formed on the work piece at an initial stage of the form rolling process is not stabilized. Further, according to circumstances, there is a drawback that each time an addendum portion of a die contacts a work piece, a position of an indentation deviates in a circumferential direction. In those circumstances, in addition to a configuration of the indentation portion being formed in an inappropriate shape, a precision of a gear is decreased and a gear having inferior mechanical characteristics may be formed because a base material of the work piece is unnecessarily plastically deformed.
In order to solve the foregoing drawbacks, for example, JPH1-37800U (i.e., referred to as Patent reference 1) discloses a die provided with processing teeth including a contacting portion, a mid finishing portion, a finishing portion, and a run-off portion, in order. With the construction of the die disclosed in the Patent reference 1, configurations of an addendum portion of each portion and a distance between teeth portions are changed. Thus, when pressing the die into the work piece, the addendum portion of the die can be pressed to a desired position to form an indentation in an appropriate configuration. Other than the disclosure in the Patent reference 1, for example, according to a known method, in response to a distance between an axial center of a die and an axial center of a work piece is shortened, dies are changed to perform the form rolling. According to this method, although a gear is formed to some extent with precision, changing operations of dies require man-hours and labors.
As explained above, in known methods, the pressed positions of the die change when performing a form rolling using a round die, and configurations of teeth of the die are configured to change during the form rolling process in order to compensate for the changes of the pressed positions of the die. Accordingly, manufacturing operations of the gear are assumed to be complicated and man-hours and manufacturing costs are increased.
A need thus exists for a form rolling method for an involute gear which is not susceptible to the drawback mentioned above.